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integral Derivatives and introduction to anti-derivatives.

Derivatives

If you want an introduction to anti-derivatives then skip to here: Anti-derivatives

Otherwise continue from here.

To put it simply a derivative is rate of change. As we know the formula for slope is change in y divided by change in x.

m=δyδx m=\frac{\delta{y}}{\delta{x}}

m is slope, Delta y is change in y, Delta x is change in x. The Delta symbol can be changed to the letter D

m=DyDx m=\frac{Dy}{Dx}

Thus this is identical to slope. The second derivative of x is also Dy/Dx and thus the second derivative of x is slope.